As wireless communication systems evolve, the transition from homogeneous structures to heterogeneous ones intensifies. The need for continuous connectivity, fairness, and spectrum efficiency, such as in massive Internet of Things (IoT) networks and ultra reliable low latency communications (uRLLC), necessitates the utilization of base stations with diverse capabilities and coverage areas. As a result, the need for advanced interference management, user-cell association, and resource allocation techniques increases. This study proposes an innovative solution for the problem of non-orthogonal multiple access (NOMA) user-cell association in multi-tier ultra-dense heterogeneous networks (UD-HetNet). The proposed network constitutes a general framework that can be applied to next generation cellular communications, massive IoT, non-terrestrial and uRLLC type communications. Differing from previous studies that ignore interference and primarily focus on the received signal powers for user-cell association, this investigation advances the subject by considering the interplay between downlink received signal/interference power and uplink inter-cell interference. Due to the non-convex integer programming nature of the problem, it is proposed to employ an innovative relaxation algorithm to obtain a sub-optimal solution for the total signal-to-interference-plus-noise ratio (SINR). As verified through simulation results, the proposed association method permits concurrent communication participation of multiple users while managing the interference, rendering it as an ideal approach for systems emphasizing fairness and continuous connectivity.